1. ## Partial fractions

I'm trying to evaluate an integral of a rational function, but I'm wondering if the following step is correct:

$\displaystyle $\frac{x^2}{\left (x^2-9 \right )^2}=\frac{1/3}{x+3}+\frac{1/4}{\left (x+3 \right )^2}+\frac{1/2}{x-3}+\frac{1/4}{\left ( x-3 \right )^2}$$

2. You can always get common denominators on the RHS, add them up, and see if you get the LHS as a check on your method. What do you get when you do that?

3. Ooops, it's suppose to be $\displaystyle $\frac{x^2}{\left (x^2-9 \right )^2}=-\frac{1/12}{x+3}+\frac{1/4}{\left (x+3 \right )^2}+\frac{1/12}{x-3}+\frac{1/4}{\left ( x-3 \right )^2}$$.

4. That's correct.